Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2	, ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5	, ⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 11, 7, 51, 13, 8, 15, 16, 17, 14, 18	, ⊢
	: , : , : , : , : , : , :
5	instantiation	9, 51, 10, 11, 12, 13, 14, 15, 16, 17, 18	, ⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
8	instantiation	19	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.association
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	instantiation	20	⊢
	: , : , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	49, 24, 21	⊢
	: , : , :
15	instantiation	49, 24, 22	⊢
	: , : , :
16	instantiation	49, 24, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
18	instantiation	49, 24, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
21	instantiation	49, 30, 26	⊢
	: , : , :
22	instantiation	49, 30, 27	⊢
	: , : , :
23	instantiation	49, 28, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
25	instantiation	49, 30, 31	⊢
	: , : , :
26	instantiation	49, 34, 32	⊢
	: , : , :
27	instantiation	49, 34, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
31	instantiation	49, 34, 35	⊢
	: , : , :
32	instantiation	49, 36, 37	⊢
	: , : , :
33	instantiation	49, 50, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
35	assumption		⊢
36	instantiation	39, 40, 41	⊢
	: , :
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
40	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
41	instantiation	42, 43, 44	⊢
	: , :
42	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
43	instantiation	49, 45, 46	⊢
	: , : , :
44	instantiation	47, 48	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
46	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
47	theorem		⊢
	proveit.numbers.negation.int_closure
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1